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Pro-aperiodic monoids via saturated models. (English) Zbl 1402.68126

Vollmer, Heribert (ed.) et al., 34th symposium on theoretical aspects of computer science (STACS 2017), Hannover, Germany, March 8–11, 2017. Proceedings. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik (ISBN 978-3-95977-028-6). LIPIcs – Leibniz International Proceedings in Informatics 66, Article 39, 14 p. (2017).
Summary: We apply Stone duality and model theory to study the structure theory of free pro-aperiodic monoids. Stone duality implies that elements of the free pro-aperiodic monoid may be viewed as elementary equivalence classes of pseudofinite words. Model theory provides us with saturated words in each such class, i.e., words in which all possible factorizations are realized. We give several applications of this new approach, including a solution to the word problem for \(\omega\)-terms that avoids using McCammond’s normal forms, as well as new proofs and extensions of other structural results concerning free pro-aperiodic monoids.
For the entire collection see [Zbl 1360.68020].

MSC:

68Q70 Algebraic theory of languages and automata
03C50 Models with special properties (saturated, rigid, etc.)
06E15 Stone spaces (Boolean spaces) and related structures
20M05 Free semigroups, generators and relations, word problems
20M35 Semigroups in automata theory, linguistics, etc.
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